\[\begin{array}{l}
a)3X(x - 1) + x - 1 = 0\\
\Leftrightarrow \left( {x - 1} \right)\left( {3{\rm{x}} + 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 1 = 0\\
3{\rm{x}} + 1 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = \frac{{ - 1}}{3}
\end{array} \right.\\
Vay:S = \{ 1;\frac{{ - 1}}{3}\} \\
b)8{x^3} - 50x = 0\\
\Leftrightarrow 2{\rm{x}}\left( {4{{\rm{x}}^2} - 25} \right) = 0\\
\Leftrightarrow 2{\rm{x}}\left( {2{\rm{x}} - 5} \right)\left( {2{\rm{x}} + 5} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
2{\rm{x}} = 0\\
2{\rm{x}} - 5 = 0\\
2{\rm{x}} + 5 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = \frac{5}{2}\\
x = \frac{{ - 5}}{2}
\end{array} \right.\\
Vay:S = \{ 0;\frac{5}{2};\frac{{ - 5}}{2}\} \\
c){(2x - 1)^2} - 25 = 0\\
\Leftrightarrow \left( {2{\rm{x}} - 1 - 5} \right)\left( {2{\rm{x}} - 1 + 5} \right) = 0\\
\Leftrightarrow \left( {2{\rm{x}} - 6} \right)\left( {2{\rm{x}} + 4} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
2{\rm{x}} - 6 = 0\\
2{\rm{x}} + 4 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = - 2
\end{array} \right.\\
vay:S = \{ 3; - 2\} \\
d)2(x + 3) - {x^2} - 3x = 0\\
\Leftrightarrow 2\left( {x + 3} \right) - x\left( {x + 3} \right) = 0\\
\Leftrightarrow \left( {x + 3} \right)\left( {2 - x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x + 3 = 0\\
2 - x = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 3\\
x = 2
\end{array} \right.\\
Vay:S = \{ - 3;2\} \\
e){(4x - 3)^2} - 3x(3 - 4x) = 0\\
\Leftrightarrow {\left( {4{\rm{x}} - 3} \right)^2} + 3{\rm{x}}\left( {4{\rm{x}} - 3} \right) = 0\\
\Leftrightarrow \left( {4{\rm{x}} - 3} \right)\left( {4{\rm{x}} - 3 + 3{\rm{x}}} \right) = 0\\
\Leftrightarrow \left( {4{\rm{x}} - 3} \right)\left( {7{\rm{x}} - 3} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
4{\rm{x}} - 3 = 0\\
7{\rm{x}} - 3 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{3}{4}\\
x = \frac{3}{7}
\end{array} \right.\\
Vay:S = \{ \frac{3}{4};\frac{3}{7}\} \\
f)4{x^2} - 25 - (2x - 5)(2x + 7) = 0\\
\Leftrightarrow \left( {2{\rm{x}} - 5} \right)\left( {2{\rm{x}} + 5} \right) - \left( {2{\rm{x}} - 5} \right)\left( {2{\rm{x}} + 7} \right) = 0\\
\Leftrightarrow \left( {2{\rm{x}} - 5} \right)\left( {2{\rm{x}} + 5 - 2{\rm{x}} - 7} \right) = 0\\
\Leftrightarrow \left( {2{\rm{x}} - 5} \right)\left( { - 2} \right) = 0\\
\Leftrightarrow 2{\rm{x}} - 5 = 0\\
\Leftrightarrow x = \frac{5}{2}\\
vay:x = \frac{5}{2}
\end{array}\]